An Introduction to Financial Option Valuation Mathematics Stochastics and Computation 1 doc
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_13 pot
... see (Iserles, 19 96; Mitchell and Griffiths,
19 80; Morton and Mayers, 19 94; Strikwerda, 19 89).
The texts (Clewlow and Strickland, 19 98; Kwok, 19 98; Wilmott, 19 98; Wilmott
et al., 19 95; Seydel, ... eliminating the W
i +1
j
terms in (24 .11 ), and the
formula then reduces to
W
i
j
= p
W
i +1
j +1
+ (1 − p
)W
i +1
j 1
, (24 .12 )
where p
=
1
2
1 +
√
k(r/...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_14 pot
... Index
dividends, 49, 18 2
double barrier option, 19 1
down -and- in call, 18 8, 18 9
down -and- in put, 19 0
down -and- out call, 18 7 18 9, 260–2 61, 265
down -and- out put, 19 0
drift, 54, 10 5, 19 8
efficient market ... neutrality, 11 5, 11 8 12 0, 14 4, 14 6, 15 1, 15 4, 16 3,
16 7, 18 0, 18 1, 19 4, 232
cash-or-nothing, 16 7 16 8
sample mean, 34, 48, 64, 14 1, 14 6...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_1 pot
... formulas
10 5
11 .1 Motivation 10 5
11 .2 Where is µ? 10 5
11 .3 Time dependency 10 6
11 .4 The big picture 10 6
11 .5 Change of variables 10 8
11 .6 Notes and references 11 1
11 .7 Program of Chapter 11 and walkthrough ... walkthrough 11 1
12 Risk neutrality 11 5
12 .1 Motivation 11 5
12 .2 Expected payoff 11 5
12 .3 Risk neutrality 11 6
12 .4 Notes and refer...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_3 pptx
... DENNEY AND STEVEN GAINES (Denney and Gaines, 2000)
36 Computer simulation
0 0.5 1
0
0.5
1
1.5
10 00 samples
0 0.5 1
0
0.5
1
1.5
10 000 samples
0 0.5 1
0
0.5
1
1.5
10 0000 samples
0 0.5 1
0
0.5
1
1.5
10 00000 ... the
U(0, 1) sample means and variances approach the true values
1
2
and
1
12
≈ 0.0833
(recall Exercise 3.5) and the N(0, 1) sample means and vari...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_4 ppt
... small,
then
e
1. 96σ
√
t+(µ−
1
2
σ
2
)t
≈ e
1. 96σ
√
t
≈ 1 − 1. 96σ
√
t
and
e
1. 96σ
√
t+(µ−
1
2
σ
2
)t
≈ e
1. 96σ
√
t
≈ 1 + 1. 96σ
√
t.
So the confidence interval is approximately
[S
0
(1 − 1. 96σ
√
t), S
0
(1 ... way to compute a quantile–quantile plot, as seen in Figures 4.4, 4.6 and
5.3. It is listed in Figure 5.4. We use MATLAB’s N(0, 1) pseudo-random number gene...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_5 ppt
... that C(S, t) in (8 .19 ) satisfies (8 .16 ), (8 .17 ) and (8 .18 ). [Hint:
to deal with (8 .16 ), take the limit t → T
−
,todeal with (8 .17 ) take the limit
S → 0
+
and to deal with (8 .18 ) take the limit ... (Bj
¨
ork, 19 98; Duffie, 20 01; Karatzas and Shreve, 19 98; Nielsen, 19 99;
Øksendal, 19 98).
It is possible to weaken the boundary conditions (8 .17 ) and (8 .18 ) in...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_7 pdf
... this model, you had these numbers,
11 .7 Program of Chapter 11 and walkthrough 11 1
11 .6 Notes and references
Colour versions of Figures 11 .3, 11 .4 and 11 .5 can be downloaded from this book’s
website, ... zlabel(’C(S,t)’)
Fig. 11 .6. Program of Chapter 11 : ch 11. m.
PROGRAMMING EXERCISES
P 11. 1. Edit ch 11. m so that it applies to a European put option, as in Figure 1...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_8 pptx
... expect
a
M
:=
1
M
M
i =1
X
i
(15 .1)
14 1
15 .6 Program of Chapter 15 and walkthrough 14 9
%CH15 Program for Chapter 15
%
% Monte Carlo for a European put
randn(’state’ ,10 0)
%%%%%%%%%%% Problem and method ... the delta.
15 .2 Monte Carlo 14 3
10
1
10
2
10
3
10
4
10
5
10
6
10
0 .1
10
0.2
10
0.3
10
0.4
Num samples
Sample mean
Fig. 15 .1. Monte Carlo approx...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_9 pot
... Ae
−r(T−t)
. (17 .10 )
17 .2. Show that C
cash
(S, t) in (17 .4) satisfies (17 .1) , (17 .2) and (17 .3).
17 .3. Differentiate (17 .4) to establish (17 .5), (17 .6) and (17 .7).
17 .4. Using (17 .4) and (17 .10 ), ... practice 15 5
Table 16 .1. European put value
approximations from binomial method
Option value
M = 10 0 1. 4 716
M = 200 1. 4762
M = 400 1. 4726
Blac...
An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_1 doc
... between 0. 01 and 0 .1 (1% and 10 %
interest rates). It is not important in this book whether D(t) is measured in dollars,
euros, or any other currency.
11
2.8 Program of Chapter 2 and walkthrough 19
0 ... 1. 4. Market values for IBM call and put options, for a range of strike prices
and times to expiry.
2.6 Upper and lower bounds on option values 15
Region for
C
0...
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